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The quantum group structure of 2D gravity and minimal models I

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Abstract

On the unit circle, an infinite family of chiral operators is constructed, whose exchange algebra is given by the universalR-matrix of the quantum groupSL(2) q . This establishes the precise connection between the chiral algebra of two dimensional gravity or minimal models and this quantum group. The method is to relate the monodromy properties of the operator differential equations satisfied by the generalized vertex operators with the exchange algebra ofSL(2) q . The formulae so derived, which generalize an earlier particular case worked out by Babelon, are remarkably compact and may be entirely written in terms of “q-deformed” factorials and binomial coefficients.

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  1. Laboratoire de Physique Théorique de l'École Normale Supérieure, 24, rue Lhomond, F-75231, Paris Cedex 05, France

    Jean-Loup Gervais

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  1. Jean-Loup Gervais
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Communicated by K. Gawedzki

Laboratoire Propre du Centre National de la Recherche Scientifique, associé à l'École Normale Supérieure et à l'Université de Paris-Sud

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Gervais, JL. The quantum group structure of 2D gravity and minimal models I. Commun.Math. Phys. 130, 257–283 (1990). https://doi.org/10.1007/BF02473353

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  • DOI: https://doi.org/10.1007/BF02473353

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